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Single Idea 14691

[filed under theme 4. Formal Logic / D. Modal Logic ML / 3. Modal Logic Systems / h. System S5 ]

Full Idea

Believers in S5 as a correct system of propositional reasoning about what might have been must claim that it is an essential property of any way things might have been that things might have been that way.

Gist of Idea

S5 believers say that-things-might-have-been-that-way is essential to ways things might have been

Source

Nathan Salmon (The Logic of What Might Have Been [1989], V)

Book Ref

Salmon,Nathan: 'Metaphysics, Mathematics and Meaning' [OUP 2005], p.145

A Reaction

Salmon is working in a view where you are probably safe to substitute 'necessary' for 'essential' without loss of meaning.

The 27 ideas from 'The Logic of What Might Have Been'

14669 For metaphysics, T may be the only correct system of modal logic [Salmon,N]
14667 System B has not been justified as fallacy-free for reasoning on what might have been [Salmon,N]
14668 In B it seems logically possible to have both p true and p is necessarily possibly false [Salmon,N]
14670 Metaphysical (alethic) modal logic concerns simple necessity and possibility (not physical, epistemic..) [Salmon,N]
14671 What is necessary is not always necessarily necessary, so S4 is fallacious [Salmon,N]
14674 Impossible worlds are also ways for things to be [Salmon,N]
14672 Possible worlds are maximal abstract ways that things might have been [Salmon,N]
14675 Possible worlds just have to be 'maximal', but they don't have to be consistent [Salmon,N]
14673 You can't define worlds as sets of propositions, and then define propositions using worlds [Salmon,N]
14676 Nomological necessity is expressed with intransitive relations in modal semantics [Salmon,N]
14678 Any property is attached to anything in some possible world, so I am a radical anti-essentialist [Salmon,N]
14677 Metaphysical necessity is said to be unrestricted necessity, true in every world whatsoever [Salmon,N]
14679 Bizarre identities are logically but not metaphysically possible, so metaphysical modality is restricted [Salmon,N]
14681 Logical necessity is free of constraints, and may accommodate all of S5 logic [Salmon,N]
14680 Logical possibility contains metaphysical possibility, which contains nomological possibility [Salmon,N]
14682 Denial of impossible worlds involves two different confusions [Salmon,N]
14687 Without impossible worlds, how things might have been is the only way for things to be [Salmon,N]
14683 Possible worlds rely on what might have been, so they can' be used to define or analyse modality [Salmon,N]
14689 Necessity and possibility are not just necessity and possibility according to the actual world [Salmon,N]
14690 In the S5 account, nested modalities may be unseen, but they are still there [Salmon,N]
14685 Metaphysical necessity is NOT truth in all (unrestricted) worlds; necessity comes first, and is restricted [Salmon,N]
14684 A world is 'accessible' to another iff the first is possible according to the second [Salmon,N]
14688 Without impossible worlds, the unrestricted modality that is metaphysical has S5 logic [Salmon,N]
14686 S5 modal logic ignores accessibility altogether [Salmon,N]
14691 S5 believers say that-things-might-have-been-that-way is essential to ways things might have been [Salmon,N]
14692 System B implies that possibly-being-realized is an essential property of the world [Salmon,N]
14693 The unsatisfactory counterpart-theory allows the retention of S5 [Salmon,N]